@Article{AAMM-16-3,
author = {Li, Congying and Tang, Liang and Zhou, Jie},
title = {Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {3},
pages = {667--691},
abstract = {<p style="text-align: justify;">In this paper, we consider two stabilized second-order semi-implicit finite
element methods for solving the Allen-Cahn and Cahn-Hilliard equations. Stabilized
semi-implicit schemes are used for temporal discretization, and the finite element
method is used for spatial discretization. It is shown that by adding a single linear
term that is of the same order with the truncation error in time, the proposed methods
are all unconditionally energy stable. Error estimates for the two schemes are also established. Numerical examples are presented to confirm the accuracy, efficiency and
stability of the proposed methods.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2023-0046},
url = {https://global-sci.com/article/90865/numerical-analysis-of-stabilized-second-order-semi-implicit-finite-element-methods-for-the-phase-field-equations}
}